R/2R digital to analog converters are well established for use in electrical circuits and particularly integrated circuits. They are simple in arrangement and can be realised to employ relatively few components and types of component having regard to the accuracy of conversion. They have inherently current switching, can be readily adapted for voltage switching and can readily be made bi-directional in operation so as to permit 2 or 4 quadrant operation.
The state of the art in relation to such converters is represented by international patent application serial number PCT/EP90/00912, (published as W090/6114).
R/2R digital to analog converters are particularly suitable for bi-polar realisation. However, the effectiveness of R/2R converters is dependent upon a precise 2:1 ratio between the impedance of a shunt arm and the impedance of a series arm. The shunt arms include a switch arrangement which is controlled by a respective component or digit of the digital signal to determine whether or not an output signal contains a component corresponding to the respective component or digit. In a normal arrangement each binary digit of the digital signal controls a switch arrangement in a respective shunt arm, such that each binary digit which is unity is represented by an appropriately scaled component of an output current, provided that, at each series node of the ladder, the impedance of the shunt arm is exactly equal to the effective series impedance presented to that node. Ideally, the switch arrangements should be composed of switches which have zero resistance when conductive, infinite impedance when non-conductive and a rapid switching time between conductive and non-conductive states. In practice, excellent switching can be achieved in a bi-polar realisation, wherein the switches in the shunt arms can be realised with a very low conductive resistance, a sufficiently rapid switching time and very low leakage when turned off. However, if the circuit is realised as an integrated circuit or part of an integrated circuit wherein the switches have a substantial resistance when conductive, the R/2R converter is less satisfactory. CMOS switches in particular have a substantial resistance when conductive, at least when normal sizes of transistor are used. Furthermore, the conductive resistance of a CMOS switch is strongly dependent upon both the voltage across the switch and the potential of the switch.
It has hitherto been proposed to compensate for these disadvantages in two general ways. One technique is to increase the passive resistances, that is to say the resistors in the series and shunt arms, so that the switch resistances are negligible in comparison to those of the resistors. Such a technique requires a large size of switch and is not satisfactory because the switches exhibit excessive parasitic impedances and operate only slowly owing to the high impedance level. A further method is to employ dummy switches, which are physically similar to the shunt switches in the series arms but which are arranged to be, effectively, permanently conductive. CMOS switches can easily be scaled in integral ratios and accordingly where a shunt switch has an aspect ratio or channel ratio of W/L, a dummy switch having a channel ratio of 2W/L, or a pair of dummy switches in parallel having a combined channel ratio of 2W/L, can be provided in the corresponding shunt arm. Alternatively the shunt switch arrangement may consist of two similar switches in series, all the switches having a channel ratio of 2W/L. In these several ways it is possible to compensate for the substantial resistance of the switches. However, none of the aforementioned techniques properly compensates for the differential non-linearity arising from the dependence of the conductive resistance of the switches on their terminal voltages.